Relational expressions to estimate the grip margin of a tire have been derived. By carrying out analysis using isotropic brush model, the grip margin was determined as functions of tire force and aligning torque. We assume quartic ground contact pressure distribution as well as conventional parabolic distribution. Using numerical examples computed by CarSim, a popular vehicle dynamics simulation software, we showed that the results of the quartic distribution gives better conformity with those of the implementation of an experimental nonlinear tire model in CarSim. On the basis of this analysis, the Chebyshev approximation of the solutions that are suitable for real time estimation has been derived.